Thus far, we have described the ordinal probit model but the framework can be
transformed into an ordinal logit model (or ordered logit
model) by simply assuming that the error follows a logistic distribution
[1]}, [2]}. Therefore, for the model in
equation (REF ), we now assume that \(\epsilon _{i} \sim L(0,1)\)  for
\(i=1,\ldots , n\) , where \(L\)  denotes a logistic distribution with mean 0 and
variance \(\pi ^{2}/3\) . Like the normal distribution, the logistic distribution
is symmetric but has heavier tails relative to a normal distribution. The
likelihood for the ordinal logit model has the same structure as
equation (REF ) with \(\Phi (w)\)  replaced by \(\Lambda (w) =\exp (w)/[1 + \exp (w)]\) , where \(w\)  is the argument inside the parenthesis.
Analogous to the ordinal probit model, the parameters are estimated using the
ML technique.
